Optical communication interface utilizing n-dimensional double square quadrature amplitude modulation

ABSTRACT

The present invention is directed to data communication system and methods. More specifically, various embodiments of the present invention provide a communication interface that is configured to transfer data at high bandwidth using nDSQ format(s) over optical communication networks. In certain embodiments, the communication interface is used by various devices, such as spine switches and leaf switches, within a spine-leaf network architecture, which allows large amount of data to be shared among servers.

CROSS-REFERENCES TO RELATED APPLICATIONS

This instant patent application claims priority to and is a divisionalof U.S. patent application Ser. No. 13/952,402, filed on Jul. 26, 2013,which claims priority to and is a continuation in part of U.S. patentapplication Ser. No. 13/791,201, filed on Mar. 8, 2013, which claimspriority to U.S. Provisional Patent Application No. 61/714,543, filedOct. 16, 2012, titled “100G PA CODED MODULATION”, and U.S. ProvisionalPatent Application No. 61/699,724, filed Sep. 11, 2012, titled “ADAPTIVEECC FOR FLASH MEMORY”, which are incorporated by reference herein forall purposes.

BACKGROUND OF THE INVENTION

The present invention is directed to data communication system andmethods.

Over the last few decades, the use of communication networks exploded.In the early days Internet, popular applications were limited to emails,bulletin board, and mostly informational and text-based web pagesurfing, and the amount of data transferred was usually relativelysmall. Today, Internet and mobile applications demand a huge amount ofbandwidth for transferring photo, video, music, and other multimediafiles. For example, a social network like Facebook processes more than500 TB of data daily. With such high demands on data and data transfer,existing data communication systems need to be improved to address theseneeds.

Over the past, there have been many types of communication systems andmethods. Unfortunately, they have been inadequate for variousapplications. Therefore, improved communication systems and methods aredesired.

BRIEF SUMMARY OF THE INVENTION

The present invention is directed to data communication system andmethods. More specifically, various embodiments of the present inventionprovide a communication interface that is configured to transfer data athigh bandwidth using nDSQ format(s) over optical communication networks.In certain embodiments, the communication interface is used by variousdevices, such as spine switches and leaf switches, within a spine-leafnetwork architecture, which allows large amount of data to be sharedamong servers.

In various embodiments of the present invention, n-dimensional DSQsymbols are optimized by reducing symbol density when mapping with PAMmappers. The reduction in symbol density can improved thesignal-to-noise ratio of the data transmitted. Depending on theimplementation, the DSQ formats, and processes thereof, can be adoptedby existing techniques and systems. There are other benefits as well.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a simplified diagram illustrating a leaf-spine architecture100 according to an embodiment of the present invention.

FIG. 2 is a simplified diagram illustrating the form factor of acommunication device according to an embodiment of the presentinvention.

FIG. 3A is a simplified diagram illustrating a communication interface300 according to an embodiment of the present invention.

FIG. 3B is a simplified diagram illustrating a segmented opticalmodulator according to an embodiment of the present invention.

FIG. 4 is a simplified block diagram illustrating the coding and mappingprocesses according to an embodiment of the present invention.

FIGS. 5A and 5B are simplified diagrams illustrating the constellationused in DSQ mapping according to embodiment of the present invention.

FIG. 6 is a simplified diagram illustrating a PAM mapping according toan embodiment of the present invention.

FIG. 7 is a simplified diagram illustrating a PAM8 mapping processaccording to an embodiment of the present invention.

FIG. 8 is a simplified diagram illustrating a PAM8 mapping process withcoded MSB and LSB bits according to an embodiment of the presentinvention.

FIGS. 9A and 9B are simplified diagram illustrating decoding process ofnDSQ symbols according to an embodiment of the present invention.

FIG. 10 is a simplified diagram illustrating a decoding nDSQ symbolswith LSB and MSB outputs according to an embodiment of the presentinvention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention is directed to data communication system andmethods. More specifically, various embodiments of the present inventionprovide a communication interface that is configured to transfer data athigh bandwidth using nDSQ format(s) over optical communication networks.In certain embodiments, the communication interface is used by variousdevices, such as spine switches and leaf switches, within a spine-leafnetwork architecture, which allows large amount of data to be sharedamong servers.

In the last decades, with advent of cloud computing and data center, theneeds for network servers have evolved. For example, the three-levelconfiguration that have been used for a long time is no longer adequateor suitable, as distributed applications require flatter networkarchitectures, where server virtualization that allows servers tooperate in parallel. For example, multiple servers can be used togetherto perform a requested task. For multiple servers to work in parallel,it is often imperative for them to be share large amount of informationamong themselves quickly, as opposed to having data going back forththrough multiple layers of network architecture (e.g., network switches,etc.).

Leaf-spine type of network architecture is provided to better allowservers to work in parallel and move data quickly among servers,offering high bandwidth and low latencies. Typically, a leaf-spinenetwork architecture uses a top-of-rack switch that can directly accessinto server nodes and links back to a set of non-blocking spine switchesthat have enough bandwidth to allow for clusters of servers to be linkedto one another and share large amount of data.

In a typical leaf-spine network today, gigabits of data are shared amongservers. In certain network architectures, network servers on the samelevel have certain peer links for data sharing. Unfortunately, thebandwidth for this type of set up is often inadequate. It is to beappreciated that embodiments of the present invention utilizes nDSQcoding in leaf-spine architecture that allows large amount (up terabytesof data at the spine level) of data to be transferred via opticalnetwork.

The following description is presented to enable one of ordinary skillin the art to make and use the invention and to incorporate it in thecontext of particular applications. Various modifications, as well as avariety of uses in different applications will be readily apparent tothose skilled in the art, and the general principles defined herein maybe applied to a wide range of embodiments. Thus, the present inventionis not intended to be limited to the embodiments presented, but is to beaccorded the widest scope consistent with the principles and novelfeatures disclosed herein.

In the following detailed description, numerous specific details are setforth in order to provide a more thorough understanding of the presentinvention. However, it will be apparent to one skilled in the art thatthe present invention may be practiced without necessarily being limitedto these specific details. In other instances, well-known structures anddevices are shown in block diagram form, rather than in detail, in orderto avoid obscuring the present invention.

The reader's attention is directed to all papers and documents which arefiled concurrently with this specification and which are open to publicinspection with this specification, and the contents of all such papersand documents are incorporated herein by reference. All the featuresdisclosed in this specification, (including any accompanying claims,abstract, and drawings) may be replaced by alternative features servingthe same, equivalent or similar purpose, unless expressly statedotherwise. Thus, unless expressly stated otherwise, each featuredisclosed is one example only of a generic series of equivalent orsimilar features.

Furthermore, any element in a claim that does not explicitly state“means for” performing a specified function, or “step for” performing aspecific function, is not to be interpreted as a “means” or “step”clause as specified in 35 U.S.C. Section 112, Paragraph 6. Inparticular, the use of “step of or” act of in the Claims herein is notintended to invoke the provisions of 35 U.S.C. 112, Paragraph 6.

Please note, if used, the labels left, right, front, back, top, bottom,forward, reverse, clockwise and counter clockwise have been used forconvenience purposes only and are not intended to imply any particularfixed direction. Instead, they are used to reflect relative locationsand/or directions between various portions of an object.

FIG. 1 is a simplified diagram illustrating a leaf-spine architecture100 according to an embodiment of the present invention. This diagram ismerely an example, which should not unduly limit the scope of theclaims. One of ordinary skill in the art would recognize manyvariations, alternatives, and modifications. The leaf-spine architecture100 comprises servers 120, leaf switches 110, and spine switches 103. Itis to be appreciated that depending on the need and specificapplication, the number and arrangement of the servers and switches maybe changed. As shown in FIG. 1, each server may be connected to morethan one leaf switch. For example, server 121 is connected to leafswitches 111 and 112. Similarly, server 122 is connected to leafswitches 111 and 112, and so is server 123. In an exemplary embodiment,server 121 is connected to the leaf switch 111 via optical communicationlink utilizing pulse amplitude modulation (PAM) and nDSQ mapping. nDSQand PAM2, PAM4, PAM8, PAM12, PAM16, and/or other variations of PAM mayalso be used in conjunction with optical communication links in variousembodiments of the present invention. The bandwidth of the opticalcommunication link between the server 121 and leaf switch 111 can beover 10 gigabits/s. Each leaf switch, such as leaf switch 111, may beconnected to 10 or more servers. In one implementation, a leaf switchhas a bandwidth of at least 100 gigabits/s.

In a specific embodiment, a leaf switch comprises a receiver deviceconfigured to receive four communication channels, and each of thechannels is capable of transferring incoming data at 25 gigabits/s andconfigured as a PAM-2 format. For example, the incoming data may bereceived from a processor via a PCI-e interface. Similarly, a server(e.g. server 121) comprises communication interface that is configuredto transmit and receive at 100 gigabits/sec (e.g., four channels at 25gigabits/s per channel), and is compatible with the communicationinterface of the leaf switches. The spine switches, similarly, comprisecommunication interfaces for transmitting and receiving data in PAMformat. The spine switches may have a large number of communicationchannels to accommodate a large number of leaf switches, each of whichprovides switching for a large number of servers.

The leaf switches are connected to spine switches. As shown in FIG. 1,each leaf switch is connected to spine switches 101 and 102. Forexample, leaf switch 111 is connected to the spine switch 101 and 102,and so are leaf switches 113 and 114. In a specific embodiment, each ofthe spine switches is configured with a bandwidth of 3.2 terabytes/s,which is big enough to communicate 32 optical communication links at 100gigabits/s each. Depending on the specific implementation, otherconfiguration and bandwidth are possible as well.

The servers, through the architecture 100 shown in FIG. 1, cancommunicate with one another efficiently with a high bandwidth. Opticalcommunication links are used between servers and leaf switches, and alsobetween leaf switches and spine switches, and PAM utilized for opticalnetwork communication.

It is to be appreciated that the PAM communication interfaces describedabove can be implemented in accordance with today communicationstandards form factors. In addition, afforded by high efficiency level,network transceivers according to embodiments of the present inventioncan have much lower power consumption and smaller form factor comparedto conventional devices. FIG. 2 is a simplified diagram illustrating theform factor of a communication device according to an embodiment of thepresent invention. Today, C form-factor pluggable (CFP) standard iswidely adapted for gigabit network systems. Conventionalelectrical-connection based CFP transceivers often use 10×10 gigabits/slines to achieve high bandwidth. With optical connection, CFPtransceivers can utilize 10×10 gigabits/s configuration, 4×25 gigabits/sconfiguration, or others. It is to be appreciated that by utilizingoptical communication link and PAM format, a transceiver according tothe present invention can have a much smaller form factor than CFP andCFP2 as shown. In various embodiments, communication interfacesaccording to the invention can have a form factor of CFP4 or QSFP, whichare much smaller in size than the CFP. In addition to smaller formfactors, the power consumption of communication interfaces according tothe present invention can be much smaller. In a specific embodiment,with the form factor of QSFP, the power consumption can be as low asabout 3 W, which is about ¼ that of convention transceivers with CFPform factor. The reduce level of power consumption helps save energy atdata centers, where thousands (sometimes millions) of thesecommunication devices are deployed.

FIG. 3A is a simplified diagram illustrating a communication interface300 according to an embodiment of the present invention. This diagram ismerely an example, which should not unduly limit the scope of theclaims. One of ordinary skill in the art would recognize manyvariations, alternatives, and modifications. The communication interface300 includes transmitter module 310 and a receiver module 320. Thetransmitter module 310 comprises a receiver 311, encoder 312, and PAMmodulation driver 313.

In an embodiment, the communication interface 300 is configured toreceive incoming data at through four channels, where each channel isconfigured at 25 gigabits/s and configured as a PAM-2 format. Using thetransmitter module 310, modulator 316, and the laser 314, thecommunication interface 300 processes data received at 25 gigabits/sfrom each of the four incoming channels, and transmits PAM modulatedoptical data stream at a bandwidth of 100 gigabits/s. It is to beappreciated that other bandwidths are possible as well, such as 40 Gbps,400 Gbps, and/or others.

As shown the transmitter module 310 receives 4 channels of data. It isto be appreciated that other variants of pulse-amplitude modulation(e.g., PAM4, PAM8, PAM12, PAM16, etc.), in addition to PAM-2 format, maybe used as well. The transmitter module 310 comprises functional block311, which includes a clock data recovery (CDR) circuit configured toreceive the incoming data from the four communication channels. Invarious embodiments, the functional block 311 further comprisesmultiplexer for combining 4 channels for data. For example, data fromthe 4 channels as shown are from the PCI-e interface 350. For example,the interface 350 is connected to one or more processors. In a specificembodiment, two 2:1 multiplexers are employed in the functional block311. For example, the data received from the four channels arehigh-speed data streams that are not accompanied by clock signals. Thereceiver 311 comprises, among other things, a clock signal that isassociated with a predetermined frequency reference value. In variousembodiments, the receiver 311 is configured to utilize a phase-lockedloop (PLL) to align the received data.

The transmitter module 310 further comprises an encoder 312. As shown inFIG. 3, the encoder 312 comprises a forward error correction (FEC)encoder. Among other things, the encoder 312 provides error detectionand/or correction as needed. For example, the data received is in aPAM-2 format as described above. The received data comprises redundancy(e.g., one or more redundant bits) helps the encoder 312 to detecterrors. In a specific embodiment, low-density parity check (LDPC) codesare used. The encoder 312 is configured to encode data received fromfour channels as shown to generate a data stream that can be transmittedthrough optical communication link at a bandwidth 100 gigabits/s (e.g.,combining 4 channels of 25 gigabits/s data). For example, each receivedis in the PAM-2 format, and the encoded data stream is a combination offour data channels and is in nDSQ format. As described in more detailsbelow, data stream is encoded into nDSQ symbols, and n is the number ofdimensions. For example, an n dimensional constellation is used formapping the data into nDSQ symbols.

The PAM modulation driver 313 is configured to drive data stream encodedby the encoder 312. In various embodiments, the receiver 311, encoder312, and the modulation driver 313 are integrated and part of thetransmitter module 310.

The PAM modulator 316 is configured to modulate signals from thetransmitter module 310, and convert the received electrical signal tooptical signal using the laser 314. For example, the modulator 316generates optical signals at a transmission rate of 100 gigabits persecond. It is to be appreciated that other rate are possible as well,such as 40 Gbps, 400 Gbps, or others. The optical signals aretransmitted in a PAM format (e.g., PAM-8 format, PAM12, PAM 16, etc.).In various embodiments, the laser 314 comprises a distributed feedback(DFB) laser. Depending on the application, other types of lasertechnology may be used as well, as such vertical cavity surface emittinglaser (VCSEL) and others.

FIG. 3B is a simplified diagram illustrating a segmented opticalmodulator according to an embodiment of the present invention. Thisdiagram is merely an example, which should not unduly limit the scope ofthe claims. One of ordinary skill in the art would recognize manyvariations, alternatives, and modifications. For example, modulated PAMsignals modulated for transmission over optical communication links.

Now referring back to FIG. 3A. The communication interface 300 isconfigured for both receiving and transmitting signals. A receivermodule 320 comprise a photo detector 321 that converts incoming datasignal in an optical format converts the optical signal to an electricalsignal. In various embodiments, the photo detector 321 comprises indiumgallium arsenide material. For example, the photo detector 321 can be asemiconductor-based photodiode, such as p-n photodiodes, p-i-nphotodiodes, avalanche photodiodes, or others. The photo detector 321 iscoupled with an amplifier 322. In various embodiments, the amplifiercomprises a linear transimpedance amplifier (TIA). It is to beappreciated by using TIA, long-range multi-mode (LRM) at high bandwidth(e.g., 100 Gb/s or even larger) can be supposed. For example, the TIAhelps compensate for optical dispersion in electrical domain usingelectrical dispersion compensation (EDC). In certain embodiments, theamplifier 322 also includes a limiting amplifier. The amplifier 322 isused to produce a signal in the electrical domain from the incomingoptical signal. In certain embodiments, further signal processing suchas clock recovery from data (CDR) performed by a phase-locked loop mayalso be applied before the data is passed on.

The amplified data signal from the amplifier 322 is processed by theanalog to digital converter (ADC) 323. In a specific embodiment, the ADC323 can be a baud rate ADC. For example, the ADC is configured toconvert the amplified signal into a digital signal formatted into a 100gigabit per second signal in a PAM format. For example, the data signalscan have nDSQ symbols representing the data stream. The functional block324 is configured to process the 100 Gb/s data stream and encode it intofour at streams at 25 Gb/s each. For example, the incoming optical datastream received by the photo detector 321 is in PAM-8 format at abandwidth of 100 Gb/s, and at block 324 four data streams in PAM-2format is generated at a bandwidth of 25 Gb/s. The four data streams aretransmitted by the transmitter 325 over 4 communication channels at 25Gb/s.

It is to be appreciated that there can be many variations to theembodiments described in FIG. 3. For example, different number ofchannels (e.g., 4, 8, 16, etc.) and different bandwidth (e.g., 10 Gb/s,40 Gb/s, 100 Gb/s, 400 Gb/s, 3.2 Tb/s, etc.) can be used as well,depending on the application (e.g., server, leaf switch, spine switch,etc.).

FIG. 4 is a simplified block diagram illustrating the coding and mappingprocesses according to an embodiment of the present invention. Thisdiagram is merely an example, which should not unduly limit the scope ofthe claims. One of ordinary skill in the art would recognize manyvariations, alternatives, and modifications. As an example, the encoder401 and the nDSQ mapper 402 are both parts of the FEC 312 in FIG. 3A. Ina specific embodiment, the encoder 401 is configured to group bits fromthe data stream as most significant bits (MSBs) and leas significantbits (LSBs). The MSBs are provided to the nDSQ mapper 402 as datablocks. The LSBs are encoded in various coding schemes. For example, theLSBs may be encoded with BCH and/or RS coding schemes.

It is to be appreciated data stream is mapped into n-dimensional doublesquare quadrature amplitude modulation (nDSQ) coded signals symbols fortransmission. It is to be appreciated by using nDSQ symbols for datatransmission, a high transmission rate can be achieved. In variousembodiments, the present invention provides techniques for nDSQ codingthat offer both high efficiency and high accuracy. FIGS. 5A and 5B is asimplified diagram illustrating the constellation used in DSQ mappingaccording to embodiment of the present invention. This diagram is merelyan example, which should not unduly limit the scope of the claims. Oneof ordinary skill in the art would recognize many variations,alternatives, and modifications. For example, a_(2k) represents a symbolin the data stream, and a_(2k+1) represents the next symbol in the datastream. As shown in FIG. 5A, DSQ32 coding with 2 dimensions is provided,and data symbols are closely packed together.

FIG. 5B illustrates DSQ32 coding where half of the data symbols areremoved. By removing every other data symbol, the distance from one datasymbol to its adjacent symbol is increased, which results in a 3 dB gainin signal-to-noise ratio (SNR). For example, the change in transmissionrate is rate=2.5 bit/symbol. The reduction of the symbols can beachieved by mapping 5 bits to 2 PAM8 symbols from the DSQ constellation.It is to be appreciated that reduction of neighboring symbols can beperformed on n dimensional DSQ constellations. For example, forthree-dimensional DSQ constellation, where axes are 3_(k), 3_(k+1),3_(k+2), the symbol density can be similarly reduced. While reducing thenumber of data symbols in a constellation would reduce data transmissionrate, the SNR is improved.

As an example, a DSQ32 can be interpreted as a (6,5) code where theparity equation is given by Equation 1 below:a _(2k) +a _(2k−1)=0 mod 2.  (Equation 1)

The PAM8 symbols can be decomposed according to Equation 2 below:a _(k) =a _(k) ^(pam4) +a _(k) ^(pam2);a _(k) ^(pam4)ε{0,2,4,6}(PAM4) and a _(k) ^(pam2)ε{0,1}(PAM2)  (Equation2)

By definition an nD-DSQ symbol of dimension dim is defined as:

${\underset{\_}{a} = \left\lbrack {a_{1},\ldots\mspace{14mu},a_{\dim}} \right\rbrack},{{{where}\mspace{14mu} a_{i}} \in {{PAN}\; 8\mspace{14mu}{and}}}$${\sum\limits_{i = 1}^{\dim}\; a_{i}} = {\left. {0\mspace{14mu}{mod}\mspace{14mu} 2}\Leftrightarrow{\sum\limits_{i = 1}^{\dim}\; a_{i}^{{pam}\; 2}} \right. = {0\mspace{14mu}{mod}\mspace{14mu} 2}}$

As implemented, the n-dimensional DSQ coding consists of mapping 3*dim−1bits to dim PAM8 symbols (being an nD-DSQ symbol). For example, thenD-DSQ coding is equivalent to 1 bit-error detection on the dim−1 LSB(PAM2) bits. The rate is Rate=3−1/dim bits/symbol. The SNR gain (perneighbor) is still 3 dB but the number of neighbors increases with dim(illustrated later on).

FIG. 6 is a simplified diagram illustrating a PAM mapping according toan embodiment of the present invention. This diagram is merely anexample, which should not unduly limit the scope of the claims. One ofordinary skill in the art would recognize many variations, alternatives,and modifications. As shown in FIG. 6, incoming bits are divided intoMSBs and LSBs. For the MSBs, (M−1)*dim number of bits are mapped by thePAM−(M−1) mapper, to provide dim PAM−(M−1) symbols. For example, themapped MSBs are in {0, 2, 4, 6, . . . M−2} format. For the LSBs, (dim−1)number of bits are processed by adding a parity bit to generate dimnumber of bits. For example, parity bit is used to remove the “odd” sumsof the LSBs such that the parity of the DSQ symbol is always even. PAM2mapping is used or the LSB bits, and the parity bit is added for errordetection purpose. The PAM2 and PAM(M−1) outputs are added together toprovide n-dimensional DSQ symbol.

FIG. 7 is a simplified diagram illustrating a PAM8 mapping processaccording to an embodiment of the present invention. This diagram ismerely an example, which should not unduly limit the scope of theclaims. One of ordinary skill in the art would recognize manyvariations, alternatives, and modifications. As shown in FIG. 7, MSBsare mapped by PAM4 Gray mapping. The LSBs is mapped by PAM2 mapping, anda parity is used to forces an even number of LSB 1's. The parity bit isused to detect single bit errors per dim bits and applies maximumlikelihood correction of single error events. The coded MSBs and LSBsare combined, which is a natural multi-level code structure. Forexample, the closest neighbors to a given nD-DSQ constellation pointcorrespond to flipping 2 bits among the LSB dim bits. This correspondsto 3 dB Euclidian distance gain compared to the uncoded case. Forexample, each nD-DSQ symbol sees an average number of neighbors boundedby:3×n_(choosek)(dim,2)

For example, the MSB bits see a 6 dB gain, given the corrected LSB bits.As dimension n increases, rate penalty ratio from the reduction ofsymbols is reduced.

As described above, before MSBs and LSBs are encoded first before mappedto DSQ symbols. FIG. 8 is a simplified diagram illustrating a PAM8mapping process with coded MSB and LSB bits according to an embodimentof the present invention. This diagram is merely an example, whichshould not unduly limit the scope of the claims. One of ordinary skillin the art would recognize many variations, alternatives, andmodifications. As shown in FIG. 8, LSBs are coded at a rate R0. Forexample, the LSBs are encoded in BCH and/or RS code. The LSB channel iscoded with a stronger code with rate R0. The MSB channel is coded with ahigher rate code R1. For high efficiency, coding for LSB and DSQ isoptimized, which depends on the nature of possible error events. Forexample, LSB may be coded with non-binary code with code symbols thatare multiple of (dim−1) bits. In a specific embodiment, the LSBs arecoded with (dim−1) interleaved binary codes. For example, interleaving(dim−1) BCH codes are provided to the PAM2 mapper for the LSBs. In aspecific embodiment, (dim−1) interleaved BCH (n,k,t) operates in theGF(2^m) codes running in parallel. For example, the BCH decoders seesindependent random single bit errors at their input, unless the channelcauses error bursts longer than dim. The rate is Rate=2R1+R0*(dim−1)/dimbits/symbol. The relationship between the BCH codes and dim is optimizedsuch that R0*(dim−1)/dim is maximized and the latency constraint is met.For example, the baud rate from coding can be 100e9*257/256/Rate. TheBCH Block Latency (BL) is n*dim/Baud_Rate. The MSB outer codecontributes to the total latency with only its processing latency indecoder.

FIGS. 9A and 9B are simplified diagram illustrating decoding process ofnDSQ symbols according to an embodiment of the present invention. Thisdiagram is merely an example, which should not unduly limit the scope ofthe claims. One of ordinary skill in the art would recognize manyvariations, alternatives, and modifications. In FIG. 9A, n-dimensionalDSQ symbols are decoded. The symbols are received through channel 901.During the transmission process through the channel 901, additive whiteGaussian noise (AWGN) may be introduced, where the SNR isSNR=E_(s)/sigma². The DSQ symbols are divided by the PAM slicer asshown, where the MSBs (e.g., 2 MSBs) are processed on the top portion,and the LSBs are processed at the bottom and decoded by a Wagnerdecoder. The example, Wagner decoder is used to extract softinformation. But it is to be understood that other types of decoders maybe used as well. For example, parity bit is used when processing theLSBs for error checking

For example, the error generation and PAM8 slicer are part of the DSPcore. In various embodiments, the error signal is used by all theadaptation loops. The XOR logic is used to determine, based on theoutput from the Wagner decoder as shown, whether there a zero. If thereis an error, the XOR logic element determines whether “1”.

FIG. 9B illustrates a nDSQ decoder where MSBs are processed by PAM4slicer. For example, the LSBs are used as input of the multiplexer 951to determine whether to add “1”. An approximation of the symbol errorrate (SER) for the nD-DSQ(dim) is given by:

${SER} \approx {3 \times \begin{pmatrix}\dim \\2\end{pmatrix} \times {Q\left( \frac{\sqrt{2}}{\sigma} \right)}}$

The factor sqrt(2) inside the Q-function refers to the 3 dB SNR gain andthe multiplicity factor 3n_(choosek)(dim,2) is the average number of ‘3dB’ neighbors per nD-DSQ symbol. As dim increase the rate=3-1/dim goesdown at the cost of lower ‘effective’ SNR gain. Depending on theapplication, the dominant error events are double bit errors per nD-DSQsymbol. For example, at 20 dB SNR, the probability of 4 errors per DSQsymbol is more than 3 order of magnitude lower than that of 2 errorsymbols. At 21 this amount to 4 orders of magnitude. An approximateexpression of the LSB bit error rate (BER) is given by:

${BER} \approx {3 \times \left( {\dim - 1} \right) \times {Q\left( \frac{\sqrt{2}}{\sigma} \right)}}$

FIG. 10 is a simplified diagram illustrating a decoding nDSQ symbolswith LSB and MSB outputs according to an embodiment of the presentinvention. This diagram is merely an example, which should not undulylimit the scope of the claims. One of ordinary skill in the art wouldrecognize many variations, alternatives, and modifications. As shown inFIG. 10, once the MSBs are de-mapped as described above, they aredecoded at a rate DEC1, and the LSBs are decoded at a rate of DEC0.

It is to be appreciated that nDSQ can be implemented in various waysaccording to the embodiments of the present invention. For example, forSNR=21 dB, the following parameters can be used:

BCH (511,367,t=16), m=9, dim=4, BL=52 ns and Baud=39.5 GHz.

BCH (511,314,t=14), m=9, dim=3, BL=39 ns and Baud=40.1 GHz.

for SNR=20.5 dB, the following parameters can be used:

BCH (511, 349, t=18), m=9, dim=3, BL=38 ns and Baud=40.8 GHz. BCH (1023,783, t=24), m=10, dim=3, BL=77 ns and Baud=40 GHz.

Typically when decoding failure happens, only one BCH has a detectabledecoding failure, (i.e. more than t+1 and less than 2t errors). Forexample, when using the decoded bits from the remaining dim−2 good BCHdecoders and re-do Wagner decoding with only 2 LSB bits per DSQ symbol,the bit belongs to the failing BCH and the DSQ parity bit. The raw biterror rate after this second Wagner decoding is reduced by 1/(dim−1) andbecomes that of 2D-DSQ32:

${BER} \approx {3 \times {Q\left( \frac{\sqrt{2}}{\sigma} \right)}}$

This process can reduce the BER at BCH output by:

$\left( \frac{1}{\dim - 1} \right)^{t + 1}$

For example, the process provides extra SNR margin at the cost of 1 moreBCH processing latency.

While the above is a full description of the specific embodiments,various modifications, alternative constructions and equivalents may beused. Therefore, the above description and illustrations should not betaken as limiting the scope of the present invention which is defined bythe appended claims.

What is claimed is:
 1. A communication device for processingn-dimensional double square quadrature amplitude modulation (nDSQ) codedsignals for pulse amplitude modulation with m levels (PAMm), the devicecomprising: a channel for receiving nDSQ symbols, the nDSQ symbolsincluding a first nDSQ symbol; a first splicer configured to divide thenDSQ symbol into a first segment representing most significant bits(MSBs) and a second segment representing least significant bits (LSBs);a decoder configured to processes the second segment and to generate anerror indication based at least on parity violation; a multiplexerconfigured to generate PAM (m/2) data using the first segment and theerror indication; and a de-mapping module configured to map the PAM(m/2) data to MSBs bits wherein n is associated with a number ofdimensions and is 2 or greater, and m is 2 or greater.
 2. The device ofclaim 1 wherein the decoder comprises a Wagner decoder.
 3. The device ofclaim 1 further comprising a second splicer for dividing the firstsegment into a third segment and a fourth segment.
 4. The device ofclaim 1 further comprising a logic element to determine whether to add“1” to the first segment based at least on the error indication.
 5. Thedevice of claim 1 further comprising (n−1) BCH decoders.
 6. The deviceof claim 1 wherein the de-mapping module is configured to perform Grayde-mapping.
 7. The device of claim 1 wherein the LSBs comprises n bits.8. The device of claim 1 further comprising: a photodetector forreceiving optical signals; a linear TIA for processing the opticalsignals; an analog-to-digital (ADC) module for converting amplifiedoptical signals to the nDSQ symbols.
 9. The device of claim 1 whereinthe LSBs and MSBs are added to a decoded data stream.
 10. The device ofclaim 1 wherein the decoder is configured to generate LSBs.